The views expressed in this article by Tuong Nhu Che do not necessarily reflect the views of the Australian Bureau of Agricultural and Resource Economics.
Author Contributions: TK designed the algorithm to solve the problem, performed the research and helped write the article, RQG performed the research, and designed and helped write the article, TNC performed the research and helped analyze the data.
Editor: Prof. Stephen Polasky
Professor R. Quentin Grafton, Crawford Building (132), Lennox Crossing, The Australian National University, Canberra, ACT 0200, Australia. Tel: +61-2-6125-6558; fax: +61-2-6125-5570; E-mail: email@example.com
Stochastic dynamic programming is used to model the world's largest fishery—tunas of the western and central Pacific—and to show that adopting a biomass target that maximizes the discounted economic profits (BMEY) from harvesting would result in larger stocks compared to de facto biological targets, and also lower catches relative to business as usual. This result is obtained for the three major tuna species, including skipjack tuna, which is not currently considered to be overfished biologically. Gains from larger tuna stocks are shown to exceed US$ 3 billion and increase the likelihood of stock rebuilding as some of these higher profits could be used to compensate fishers and countries for transitional losses to higher biomass levels. Adopting a dynamic BMEY target thus offers a potential “win-win”—better conservation outcomes with larger fish stocks and higher economic profits.
Key questions in the sustainable management of fisheries are: What should be the target biomass? How can fisheries be managed to move toward such a target? When should these targets be achieved if stock rebuilding is required? For decades fisheries managers have adopted a maximum sustained yield biomass (BMSY) as their target (Anderson et al. 2008), or used it as a limit reference point. As biological biomass targets are independent of profits, fishers frequently oppose stock rebuilding designed to achieve desirable biological reference points.
Recent modeling shows that a biomass target that maximizes the sum of the discounted net profits from fishing—the dynamic maximum economic yield biomass (BMEY)—will, under reasonable discount rates, exceed BMSY in some fisheries (Grafton et al. 2007). Factors that favor this result include a high intrinsic growth rate, a low discount rate, and the importance of stock abundance (i.e., a “stock effect”) and fishing effort on the level of harvest. Using biological and economic data from the one of the world's most valuable fisheries—the Western and Central Pacific tuna fisheries (WCPTF)—we extend Grafton et al. (2007) to account for both transitional and ongoing payoffs and calculate measures of economic profitability from adopting a dynamic BMEY target versus business-as-usual.
The main target species in the WCPTF include: skipjack tuna (Katsuwonus pelamis) caught mainly by purse seine vessels, yellowfin tuna (Thunnus albacares) caught by both purse seine and longline vessels, and bigeye tuna (T. obesus) caught predominantly by longline vessels (Williams & Reid 2006). The total harvest across all species has increased, on average, by about 5% per year over the past 50 years (Figure 1), but fishing effort has grown even faster with the total number of boat-days rising at an annual rate of about 10% per year over the period 1970–2000.
The WCPTF are collectively managed by member countries of the Western and Central Pacific Fisheries Commission (WCPFC). The multilateral compliance measures of the WCPFC include a compulsory vessel registry for fishing vessels, a vessel monitoring system that tracks their location, some observer coverage to record catches and, most recently, a scheme that tries to cap the total number of vessel days by purse seine vessels operating in the region.
A biological justification to limit fishing effort of yellowfin and bigeye has been consistently been made by the Scientific Committee of the WCPFC. Despite an acceptance of the conclusions of the Scientific Committee, key recommendations to reduce catches of yellowfin and bigeye have not yet been implemented (Langley et al. 2009). This is because many fishers, and some countries, do not consider it is in their economic interest.
To prevent further declines in profitability and to promote the sustainability of tuna stocks, at a minimum, demands that WCPFC members understand the bioeconomic costs of business-as-usual. An analysis of these costs requires: (1) dynamic BMEY targets for the main tuna species; (2) optimal transition paths in terms of the total catches of tuna over time to achieve dynamic BMEY targets; and (3) calculation of the bioeconomic losses from business-as-usual compared to profits at the dynamic BMEY targets.
To calculate the dynamic BMEY target for the major tuna species and the corresponding bioeconomic losses, a suitable biological model must be developed and connected to an economic model. Bertignac et al. (2000) provided one of the first estimates of profits in the fishery and estimated the effects of changes in fishing effort across countries. Reid et al. (2006) constructed a useful bioeconomic model of the fishery but did not provide optimal results, measures of dynamic BMEY or bioeconomic losses from not pursuing the path to BMEY or its target. Kompas & Che (2006) and Grafton et al. (2007) developed dynamic BMEY results for the fishery but did not generate path to BMEY effects, or the transitional losses from not following a path to BMEY.
The biological structure and the parameters in the dynamic bioeconomic model in this article are based on Hampton et al. (2006a, b). Quarterly cohort structures in an age-structured model are developed where the initial size of the cohorts is determined by current recruitment, after which time cohort attrition occurs due to natural and fishing mortality. The dynamic growth of each species by each cohort is modeled at quarterly time steps. Recruitment is the appearance of age-class “one” fish in the population and it is assumed that recruitment occurs instantaneously at the beginning of each quarter, following a Beverton Holt stock recruitment relationship (discrete approximation) with coefficients by species and regions based on Hampton et al. (2006a, b).
Assumptions made concerning age and growth are: (1) lengths-at-age are normally distributed for each age-class; (2) mean lengths-at-age follow a von Bertalanffy growth curve; (3) standard deviations of length for each age-class are a log-linear function of the mean lengths-at-age; and (4) the distribution of weight-at-age is a deterministic function of the length-at-age and a specified weight–length relationship. The natural mortality rate (m) is assumed to be age specific, invariant over time and region, and continuous through the time steps. The current biomass, the virgin biomass, and the current rates of exploitation of each species are estimated as the average for 2001–2004 from Hampton et al. (2006a, b) with time-series biomass data from Hampton et al. (2006a).
Let B(t+ 1) denote the fish biomass (measured in weight) at time t+ 1 be given by
where B(t) is the previous period's biomass, h(t) is the fishing mortality, d(B(t)) is the net growth of fish biomass, and f[B(t)] is the growth function of fish biomass.
The population dynamic of fish biomass or recruitment (R(t)) is measured in weight and is given by
The net growth of fish biomass δ(B(t)) is determined by
where g(B(t)) is the growth function of the biomass measured in weight from period t to t+ 1, which depends on the size of B(t) and the growth length–weight relationship; m(B(t)) is natural mortality which depends on the natural mortality rate, m, and the size of B(t) and is allowed to vary by age cohort.
Based on the stock assessment, a conversion from fish numbers to weight is required and obtained from a standard growth in length and length–weight relationship given by a von Bertalanffy formula (1938). The growth in fish length is
where l∞ defines an asymptotic or maximum body size, ki is the Brody growth coefficient, defining the growth rate toward the maximum, and t0 shifts the growth curve along the age axis to allow for apparent nonzero body length at age zero. The length–weight relationship is thus
where u and v are parameters.
Finally, the δ(B(t)) component of the net growth of fish biomass in (1) depends on the natural mortality, m, and fish density, (B(t)/B(0)). The lower is fish density the higher is net growth. At maximum density (or B(t) =B(0)) the net growth of the biomass is at minimum. The functional relationship of the net growth in the biomass is given by
where ψ and χ are parameters and ψ is estimated from R(0) and B(0). The biological model is not explicitly spatial except that it corresponds to the established zones specified in the WCPO tuna regions. Additional information on the biological model is contained in the supporting information.
At a given time t (t= 1, …, T), the harvest is denoted by hijg that indicates the harvest of species i by fleet j in area g where i= 1, 2, 3; j= 1, …, 12; and g= 1, 2, 3, i.e., there are 3 species, 12 fleets, and 3 fishing areas or zones. The harvest function of a species i by fleet j in area g at time t is given by
where q0ijg is the intercept term; Eijg(t) is the effort of fleet j to fish species i in area g; Big(t) is the biomass stock of species i in area g; and αijg and βijg are the parameters of the harvest function of fleet j for species i in area g.
The fishing effort of fleet j is measured as total effort for all species in all areas averaged over tuna caught with fishing aggregating devices and with unassociated sets. The effort allocation to a species i in area g is
where θjg is the regional effort share of fleet j to each fishing area with the constraints
The coefficient θij in (8) indicates that the effective effort allocation among species of fleet j also influences the effective fishing effort on other species, where these other species can be targeted by the same unit of nominal effort.
Total revenue of fleet j at time t (TRjt) is defined as a sum of all revenues (the product of harvest and average price) over all species and areas, i.e.,
where pij(t) is the price of species i caught by fleet j at time t. Output prices for species differ depend on the market where fish is sold, based on the analysis by Reid et al. (2003, 2006) and the Forum Fisheries Agency (2008). Fish prices used in this article are analyzed separately for the canned tuna and sashimi market.
Price elasticity measures the responsiveness of the quantity demanded of fish to a change in price that arises from a change in harvest brought to market. Price elasticities differ between the canned tuna and the fresh and frozen market. For the frozen and fresh markets, the price elasticity of demand (ɛ) for bigeye is 10 so that a 1% rise in quantity supplied to market causes a 0.1% fall in its price, and for yellowfin ɛ= 6.5. For the canned market the elasticity for skipjack is 1.9 for supply increases and 11.1 for supply decreases and is based on estimates by Pan & Pooley (2004). Further details are provided in the supporting information.
Fishing cost (including labor, material, capital, and all other costs) is a function of fishing effort defined by
where γ0jg and γ1jg are the fixed cost and variable cost parameters.
Combining Equations (7) to (11), the profit function of fleet j at time t fishing species i in area g(Πijg(t)) is defined by
Total profit of fleet j at year t(Πi(t)) is a sum of all species over all areas, or
Aggregate profit of the WCPO across all tuna species, all fleets, and all fishing areas at time t(Π (t)) until period T is thus:
where Eijg(t) is substituted from Ej(t) as indicated in (8).
The optimization problem used to calculate optimal fishing effort and dynamic BMEY maximizes the sum of expected aggregate profits through the choice of effort for each fleet, by nation, for each species in each fishing area over the planning horizon, i.e.,
where r is the discount rate and the objective function is maximized subject to (1), (7), (9), and
The value θij is the choice variable that determines Eij=E(t) θij and the optimal effort allocation to species i and fleet j. Uncertainty is added to the model in two ways: (1) by including a diffusion term in the stock transition Equation (2) of the form σB(t)κt for realization κt drawn from a normal distribution with variance σ= 0.05; and (2) by including the standard errors in the point estimates for αijg and βijg in the harvest function, or Equation (7). All reported monetary values are thus expected values conditional on the form of uncertainty. To save on notation and the complexity of the relevant expressions, these terms are not explicitly added to the equations. The supporting information reports the estimates of the harvest function.
After including random variation in relevant variables (i.e., the standard errors in coefficient values drawn from estimates of the harvest function by region) and a diffusion process for the biomass it is not possible to find an analytical solution to (15). Instead, the solution is obtained using a perturbation method (see Judd (1998)) to maximize the value function given by (15), subject to (1), (7), (9), and (16), accounting for the potential “stock effect” implied by the nonlinear harvest function. It is the stock effect (implying that either harvest or costs are stock dependent) that ensures that the dynamic version of BMEY coincides with stock values that are larger than stock at BMEY, with the share coefficient on the stock term in the harvest function, or βijg, determining a “marginal stock effect.” A terminal condition is chosen so that discounted profits become zero at the terminal point. The planning horizon for the optimization procedure is chosen to ensure that the optimal path maximizes profits over a sufficiently long period of time (i.e., what in a deterministic model would be a near steady state) before stocks are drawn down to satisfy the terminal condition. All results are drawn from the resulting optimal path.
To implement and solve the problem specified by (15), and the associated constraints, we use previously estimated or calculated biological and price parameters, and specifically estimated (see the supporting information) parameters for the harvest function (q0ijg, αijg, and βijg). Selected estimates for the purse seine fleet and the longline fleet are provided in Table 1. Cost parameters of fleet j in area g, denoted by γ0jg and γ1jg, are provided in Table 2, and are based on Reid et al. (2003) and Reid et al. (2006). Additional information is contained in the supporting information.
Table 1. Parameter estimates of the harvest function (biomass estimates to 2002, variable years by zone, from 1972, see supporting information)
1. Fishing effort defined in vessel days for the purse seine fleet.
2. Fishing effort defined in thousand hooks for the longline fleet.
3. Biomass defined in tonnes.
***Statistically significant from zero at 1% level of significance.
**Statistically significant from zero at 5% level of significance.
*Statistically significant from zero at 10% level of significance.
Purse seine fleet (zone 3)
Fishing effort (E)
Purse seine fleet (zone 4)
Fishing effort (E)
Longline fleet (zones 3 and 4)
Fishing effort (E)
Table 2. Fishing costs and fish prices by fleets and species (2006 prices US$)
Cost parameter ($/effort unit)
Fish prices ($/ton)
Purse seine ($US/ day)
Philippines and others
Frozen tuna longline ($US/hook)
Philippines and others
Fresh tuna longline ($US/hook)
PICs and others
To calculate the bioeconomic losses from business as usual versus managing the fisheries at their dynamic BMEY, we employ a planning period of 50 years, with base the year 2006, but project our model with starting values from 2008, applying a discount rate of 5%. (See Gault et al. (2008) on the problematic use of discount rates with highly valued natural resources.) In the base year, total expected profits for purse seine, frozen longline and fresh longline fleets are calculated at $93 million, $120 million, and $109 million dollars (in 2008 prices) and levels of fishing effort in all other periods are compared to the effort levels in 2006 (100 = effort level in 2006).
Table 3 summarizes the differences between the base year and dynamic BMEY target effort levels in the first 5 years (2008–2012) and when the BMEY target has been achieved. It also compares the dynamic BMEY target with BMSY—the default biological reference point for the WCPFC and dynamic BMEY to the current biomass (BCUR). The results show that in the first 5 years of the planning period (2008–2012) fishing effort for purse seine, frozen longline, and fresh longline needs to be reduced to 44%, 40%, and 51%, respectively, of their base levels. Important shifts in fishing effort between species are also required to maximize the sum of discounted economic profits from fishing over time.
Table 3. Results for optimal solutions (discount rate = 0.05)
Optimal effort level as % of base year value (= 100)
2. Dynamic MEY/Current biomass ratio based on business-as-usual projections for the current biomass to 2008 from a 2006 base year.
In the first 5 years
In the first 5 years
In the first 5 years
Dynamic MEY biomass/ MSY biomass
Dynamic MEY/Current biomass
The results in Table 3 show that the dynamic BMEY target is larger than BMSY for yellowfin, bigeye, and skipjack tuna. This is because a larger biomass makes it easier to find and catch fish that lowers per unit harvesting costs and increases expected profits. Given the price elasticity of demand, a lower catch also increases the price of fish.
The finding that dynamic BMEY > BMSY for all tuna species shows that although skipjack tuna is not currently overfished biologically, it is overexploited in an economic sense. Yellowfin tuna and bigeye tuna are overexploited in an economic sense because BMEY > BCUR and are also overfished biologically because current fishing mortality exceeds the fishing mortality at BMSY (Langley et al. 2009).
Sensitivity results on the values of BMEY to BMSY, in terms of changes in parameter values for the stock coefficient, average tuna prices, and the costs of fishing are reported in the supporting information.
The net expected present value of profits is the sum of the discounted annual expected profit from fishing in U.S. dollars and is calculated for each period in the 50-year planning horizon for two scenarios. The dynamic BMEY scenario represents the optimal transition path to the dynamic BMEY target while the business-as-usual scenario assumes that the base-year levels of fishing effort for each fleet are maintained. A comparison of the net present value of profits of the two scenarios across all tuna species for the 50-year planning period is presented in Figure 2.
Stock rebuilding associated with the transition to the dynamic BMEY target results in initially lower profits compared to business-as-usual for the first 3 years. Thereafter, after the biomass of the tunas has increased, the transition to the dynamic BMEY target generates higher expected profits than business-as-usual. The net present value of expected profits is maximized with the dynamic BMEY target between 10 and 12 years. It declines thereafter because of the impact of discounting and not because of any reduction in the biomass or profitability in nominal dollar terms. The integral of the areas between the two curves represents the bioeconomic losses from business-as-usual compared to adopting a dynamic BMEY target.
If the tuna fisheries were managed according to the dynamic BMEY target the cumulative expected net present value over the entire planning period is $5.4 billion or about $108 million per year. If the fishery follows the business-as-usual path (not including losses after year 35), the cumulative expected net present value with business-as-usual is $2.0 billion, or about $57 million per year. Thus, the bioeconomic losses from business-as-usual are approximately $3.4 billion. This result varies relative to sensitivity on parameter values as reported in the supporting information, from $1.9 to $4.8 billion, but the main point still stands. Business-as-usual results in large economic losses relative to optimal harvesting.
The results provide both an economic and a biological justification for reducing current fishing effort and increasing biomass levels of all tunas (including skipjack tuna) in the world's largest fishery. Higher future profits can be used to compensate fishers fully for initially lower harvests and net returns as stocks transition to higher biomass. Profits could also be used to finance transfers of funds to some countries, or possibly via the transfer of annual harvest allocations (Chand et al. 2003; Munro & van Houtte 2004; Grafton et al. 2010) to help ensure support for lower overall catches. A continuation of business-as-usual in the tuna fisheries will not only generate much lower profits relative to a dynamic maximum economic yield target, but will also jeopardize the conservation of yellowfin and bigeye tuna stocks.
The authors are grateful for the helpful comments of two referees and an editor. The authors gratefully acknowledge partial funding for this research that was provided by AusAid under agreement 50142.